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Polytope of Type {6,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,2}*576a
if this polytope has a name.
Group : SmallGroup(576,8659)
Rank : 4
Schlafli Type : {6,6,2}
Number of vertices, edges, etc : 24, 72, 24, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,6,2,2} of size 1152
   {6,6,2,3} of size 1728
Vertex Figure Of :
   {2,6,6,2} of size 1152
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,3,2}*288
   3-fold quotients : {6,6,2}*192
   4-fold quotients : {6,6,2}*144b
   6-fold quotients : {3,6,2}*96, {6,3,2}*96
   8-fold quotients : {6,3,2}*72
   12-fold quotients : {3,3,2}*48, {2,6,2}*48
   24-fold quotients : {2,3,2}*24
   36-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,12,2}*1152a, {6,6,4}*1152e, {12,6,2}*1152c, {6,6,2}*1152a, {6,12,2}*1152d, {12,6,2}*1152e
   3-fold covers : {6,18,2}*1728, {6,6,2}*1728b, {6,6,6}*1728d, {6,6,6}*1728e, {6,6,2}*1728c
Permutation Representation (GAP) :
s0 := ( 2, 3)( 6, 7)(10,11)(13,25)(14,27)(15,26)(16,28)(17,29)(18,31)(19,30)
(20,32)(21,33)(22,35)(23,34)(24,36)(38,39)(42,43)(46,47)(49,61)(50,63)(51,62)
(52,64)(53,65)(54,67)(55,66)(56,68)(57,69)(58,71)(59,70)(60,72);;
s1 := ( 1,13)( 2,14)( 3,16)( 4,15)( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)(10,18)
(11,20)(12,19)(27,28)(29,33)(30,34)(31,36)(32,35)(37,49)(38,50)(39,52)(40,51)
(41,57)(42,58)(43,60)(44,59)(45,53)(46,54)(47,56)(48,55)(63,64)(65,69)(66,70)
(67,72)(68,71);;
s2 := ( 1,44)( 2,42)( 3,43)( 4,41)( 5,40)( 6,38)( 7,39)( 8,37)( 9,48)(10,46)
(11,47)(12,45)(13,68)(14,66)(15,67)(16,65)(17,64)(18,62)(19,63)(20,61)(21,72)
(22,70)(23,71)(24,69)(25,56)(26,54)(27,55)(28,53)(29,52)(30,50)(31,51)(32,49)
(33,60)(34,58)(35,59)(36,57);;
s3 := (73,74);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(74)!( 2, 3)( 6, 7)(10,11)(13,25)(14,27)(15,26)(16,28)(17,29)(18,31)
(19,30)(20,32)(21,33)(22,35)(23,34)(24,36)(38,39)(42,43)(46,47)(49,61)(50,63)
(51,62)(52,64)(53,65)(54,67)(55,66)(56,68)(57,69)(58,71)(59,70)(60,72);
s1 := Sym(74)!( 1,13)( 2,14)( 3,16)( 4,15)( 5,21)( 6,22)( 7,24)( 8,23)( 9,17)
(10,18)(11,20)(12,19)(27,28)(29,33)(30,34)(31,36)(32,35)(37,49)(38,50)(39,52)
(40,51)(41,57)(42,58)(43,60)(44,59)(45,53)(46,54)(47,56)(48,55)(63,64)(65,69)
(66,70)(67,72)(68,71);
s2 := Sym(74)!( 1,44)( 2,42)( 3,43)( 4,41)( 5,40)( 6,38)( 7,39)( 8,37)( 9,48)
(10,46)(11,47)(12,45)(13,68)(14,66)(15,67)(16,65)(17,64)(18,62)(19,63)(20,61)
(21,72)(22,70)(23,71)(24,69)(25,56)(26,54)(27,55)(28,53)(29,52)(30,50)(31,51)
(32,49)(33,60)(34,58)(35,59)(36,57);
s3 := Sym(74)!(73,74);
poly := sub<Sym(74)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1 >; 
 

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